#14514956

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	D₄×A₅
commutator	#6732	C₂×C₄
Frattini, cosocle	C₂×C₄	C₂²×A₅
Fitting, hypercenter	#102	A₅
prime radical	C₂×#91881	C₂
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #102

341 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 341 conjugacy classes of subgroups — too many to draw. Only its 25 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 192

Permutation generators:

(1,54,2,53)(3,56,4,55)(5,98,9,104,15,57,27,61,34,67,20,79,32,86,37,72,45,84,51,89,6,97,10,103,16,58,28,62,33,68,19,80,31,85,38,71,46,83,52,90)(7,99,12,101,14,59,25,64,36,66,17,77,30,88,39,69,48,82,50,91,8,100,11,102,13,60,26,63,35,65,18,78,29,87,40,70,47,81,49,92)(21,74,44,95,22,73,43,96)(23,76,41,94,24,75,42,93);(1,55)(2,56)(3,54)(4,53)(5,103,21,79,15,59,50,75,25,66)(6,104,22,80,16,60,49,76,26,65)(7,101,23,78,14,58,51,74,27,68)(8,102,24,77,13,57,52,73,28,67)(9,63)(10,64)(11,62)(12,61)(17,87,41,100,39,72,33,96,45,89)(18,88,42,99,40,71,34,95,46,90)(19,85,43,97,38,69,36,93,47,91)(20,86,44,98,37,70,35,94,48,92)(29,84)(30,83)(31,81)(32,82)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240654);